Translation:He's not at home now because he's getting a haircut.
'Getting one's hair cut' is an equivalent in English to 'getting a haircut'. That's why 'he's getting his hair cut' should be an equivalent to 'he's getting a haircut', even though there is no 'he' in the sentence on a literal level. It's an idiomatic expression.
"Go home" versus "I am AT home". It should be this way, isn't it. There is no logic in the English translations. Sometime it is proper English sometimes slang...